A with all instruments, we have to attach the fixed end of the string first. On a
banjo that means dealing with the tailpiece.

Tailpieces have been made in an endless variety.

Some are very simple, like this S.S.Stewart "Common Sense" tailpiece:
Here, the strings are simply tied on. Or, in the case of steel strings with loop
ends, they are cinched on by passing the string through the loop. This and many other
very early tailpieces were originally designed for gut strings.

Some tailpieces have covers over the string ends:

Some don't:
This one is very heavy and adjustable in all directions.

All tailpieces that have a long reach like these are designed to hold the strings
down toward the head, some more than others. That means that they all should be strung
in such a way that the string comes out from under the front edge. So, the string
hooks around the corner passes up over the top, and down through, or around something
at the end to hold the string downward:

It may seem simple presented this way, but in the heat of dealing with unruly strings,
some folks get a bit confused and run the string out over the top, losing the effect
of the length of the tailpiece.

The first thing to do is to make sure the loop fits over the hook on the tailpiece.
Some tailpieces, such as the heavy one above, have very large hooks and the loop
must be made a little wider to fit. That's easy, just stick a pencil through and
make the loop more round: